As a freshman, Jasper was chosen to start as coach Tubby Smith's point guard. He ultimately started the final 27 games of the 2006–07 season. UK won its first 11 games with Jasper as a starter.[9]
Over the summer, he had microfracture surgery performed on his left knee[10] and missed the first 10 games of the 2007–08 season. When he returned to action, he was the Wildcats' sixth man until freshman star Patrick Patterson would sit the rest of the season with a stress fracture in his ankle. After Patterson's injury, Jasper would take his place in the lineup. His final game with Kentucky would be played in the first round of the 2008 NCAA Tournament vs. the Marquette Golden Eagles.[11]
Jasper earned SEC Academic Honor Roll status in 2008.[12]
In May 2008, rumors circulated that Jasper was transferring from Kentucky to a school closer to his Paso Robles, California home. The schools that were named as his possible destinations were UNLV, California and UCLA. This proved to be true when he asked for his release from the team in June. Jasper said, "My transfer is no indication of my experience here; I like the direction they're headed in - it's just that I would like to attend a place closer to my home."
Jasper transferred to UNLV to play for head coach Lon Kruger. He said he liked how he fit in with the team and how Kruger motivated his players. He sat out the 2008–09 season because of NCAA transfer rules.
In October 2009, Jasper was selected as the Preseason Mountain West Conference Newcomer of the Year.[13] He then started at guard for the Runnin' Rebels, and notably led the team to wins against 16th-ranked Louisville and No. 15 New Mexico,[14] and earned his first double-double in college in a win over Tulsa at the 76 Classic in Anaheim.[15] Jasper sustained a sprained MCL to his left knee in 2010, however, sidelining him for five weeks.[16]